Subject: [mg72000] Re: [mg71957] How can I get this spiked Integral evaluated???

From: Bob Hanlon <hanlonr at cox.net>

Date: Thu, 7 Dec 2006 06:26:20 -0500 (EST)

Reply-to: hanlonr at cox.net

Integrate[Exp[-x^2], {x, -900, 1000}]
(1/2)*Sqrt[Pi]*(Erf[900] + Erf[1000])
%//N
1.77245
NIntegrate[Exp[-x^2], {x, -900, 1000},WorkingPrecision->65,MaxRecursion->15]
1.7724538509055160272981674833411451827975494561223871282
Bob Hanlon
---- Zeno <zeno333 at mindspring.com> wrote:
> This is an integral with a spike that is not in the middle of the
> integral range. Here is the integral...
>
> NIntegrate[Exp[-x^2], {x, -900, 1000}]
>
> Mathemtaica 5.2.2 gives this error message....
>
> "Numerical \integration stopping due to loss of precision. Achieved
> neither the requested \PrecisionGoal nor AccuracyGoal; suspect one of
> the following: highly \oscillatory integrand or the true value of the
> integral is 0. If your \integrand is oscillatory on a (semi-)infinite
> interval try using the option \Method->Oscillatory in NIntegrate.
> MoreÅ
>
> However, to use the option "Method->Oscillatory" one of the bounds of
> the integral must be infinity, so that would not work here. How do I
> get it to to the integral in the range -900 to 1000??
> The correct answer is 1.77245.
>